The question of whether countries experience productivity gains from foreign direct investment is still not squarely settled. Much of the empirical literature that attempts to answer this question is unable to find evidence for productivity gains in the aggregate country-level data, and is instead forced to consider disaggregated industry or firm-level data for a particular country. My paper attempts to fill this gap by combining disaggregated data for a large cross-section of countries. In it, I first present a two-country Dornbusch-Fischer-Samuelson model, in which each production sector uses labor and an intermediate services input. Moreover, each production sector combines the services input with the labor input in a unique way. I show that when labor productivity in services increases, this has two opposite effects on productivity measured in the aggregate. Firstly, the increase in labor productivity allows certain production sectors in the innovating country to become more competitive, and export more. These also happen to be the sectors which use the services input most intensively. But, on the other hand, the productivity shock also raises the economy-wide real wage, causing the real exchange rate to appreciate, and rendering certain sectors which were exporting before, to now become producers only for the domestic market. Thus, if we were to measure the impact of the productivity increase in services by looking at aggregate measures of the domestic economy's trade, our findings are likely to be biased towards finding no effect. On the other hand, a look at more disaggregated data may allow us to measure the productivity benefits more clearly. With this idea in mind, I proceed to the data. I compile a dataset comprising 40 developing countries for the year 2004. For each country, I compute, from social accounting matrices, the services usage intensity of different manufacturing sectors in that country. Also, from social accounting matrices, I compute the share of each manufacturing sector's output that the sector exports. From a separate source (Golub, 2006), I obtain an index of FDI restrictions for each service sector for each of my 40 countries. Using these pieces of data, I am able to demonstrate that when a country restricts FDI more severely in a particular services sector (say, business services, for example), then the manufacturing sectors which use that service more intensively, are able to export a smaller share of their output. This result stands up to various kinds of robustness tests, and provides strong evidence for inter-sectoral spillover benefits from FDI in services.